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Saturday, January 31, 2015

Photo Electric Effect Problems and Solutions

The phenomenon of emission of electrons from a metal surface when a light of suitable frequency incident of the metal surface is called photo electric effect.

Problem and solution

A metal of work function of 4 electron volts is exposed to
radiation of the wavelength 140 nm. What is the corresponding stopping
potential?

We can solve this problem basing on the very definition of
energy. It is written basing on plank’s quantum concept. We can further write
photo electric equation to solve the problem as shown below.

Problem and solution

On the cathode of a photoelectric cell two different
wavelengths of light are allowed to incident. The work function of the metal
surface is given. A uniform magnetic field of known magnetic field strength is
applied perpendicular to the cell. Find the radius of circular path described
by the photo electrons?

To solve this problem, first of all we have to analyse
whether the incident light is sufficient enough energy for the emission of
photo electrons or not.

It is mathematically observed that photo electric effect is
possible only with the first wavelength but not with the second wavelength. It
is simply because the wavelength and the second case is more than the threshold
wavelength.

We shall also know that whenever a magnetic field is applied
perpendicular plane, the charged particle like electron takes a circular path
and the necessary centripetal forces provided by the force due to the magnetic
field on the charger particles.

The problem is solved as shown below.

Problem and solution

If the wavelength of the incident radiation changes from one
value to other value, the corresponding kinetic energy emitted by the photo
electrons also changes from one value to other value. What is the work function
of the metal surface?

In solving this problem, we can use photo electric equation.
According to this equation the total energy supplied by the photo is equal to
sum of work function and the kinetic energy of the electron. By applying this
condition for both the cases and by simplifying the equation we can derive the
equation further work function as shown below.

Problem and solution

For a certain metal threshold frequency is given. When the
incident frequency is doubled the threshold frequency, electrons comes out with
a certain velocity. If the incident frequency is five times threshold
frequency, what is the velocity with which the electrons come out?

We can solve this problem also basing on photo electric
equation. We know that the kinetic energy of the electron emitted is equal to
the difference between the energy of the incident photon and the work function.
By substituting this condition for both the cases, cases that are given in the
problem, we can solve it.

Problem and solution

Photo electric effect from a metallic surface is observed
from two different frequencies where first frequency is greater than that of
the second frequency. If the ratio of the maximum kinetic energy emitted by the
photo electrons in both the cases is given, find the threshold frequency of the
metal surface?

We know that the incident energy of the photon is equal to
sum of work function and the kinetic energy. Applying this concept for both the
frequencies that are given, we can calculate the threshold frequency as shown
below.

Problem and solution

A photon of known energy ejects photo electrons from metal
surface with a certain work function. If this emitted electron enters into a
uniform magnetic field of known induction perpendicular to the field, what is
the radius of the circular path taken by it?

As the total energy of the photon is equal to sum of work
function and kinetic energy, we can write the equation for the velocity of the
ejected electron as shown below. This electron that is entering into the
magnetic field perpendicularly shall experience a centripetal force and shall take
a circular path. The necessary centripetal forces provided by the force
experienced by the electron due to the magnetic field.

Problem and solution

When a light of known wavelength incident on a photoelectric
surface, the velocity of the fastest electron emitted is V . If
the incident wavelength is 75% of the initial wavelength, what will be the
velocity of the emitted electron?

We can solve this problem basing on photo electric equation.
According to this equation the total energy supplied by the light in the form
of photon, is equal to sum of work function as well as the kinetic energy of
emitted electron. By substituting the given values in this equation, we can get
to equations. By solving that to equations we can identify the relation between
the last of the electron in the second case with respect to the velocity of the
electron in the first case.

Problem and solution

Here we are going to solve a simple problems basing on photo
electric effect.

When a radiation of certain wavelength is incident on a
metallic surface, the stopping potentially is found to be 4.8 V. If the same
surface is illuminated by the radiation of double the wavelength, the stopping
potential is found to be 1.6 V. What is the threshold wavelength of the
surface?

We can solve this problem basing on Einstein’s photo electric equation. According to this
equation the total energy supplied by the photon is equal to sum of work
function and kinetic energy. By applying the given data in this equation in two
different cases and by simplifying the equation is we can solve the problem as
shown below.